The Dykstra-Parsons method is often used to study the displacement of oil by water or gas in stratified reservoirs. These strata of different permeability are assumed to exhibit lateral continuity throughout the reservoir. In the proposed model, these strata are assumed to consist of several blocks with different transmissibility, kh/, and storage, c h. According to Dykstra and Parsons, the displacing fluid sweeps faster through the more permeable zones so that much of the oil in the less permeable layers must be produced over a long period of time at high WOR. In this study, it is found that this is not necessarily true. It simply depends on the rock characteristics from layer-to-layer and from block-to-block. It is also found that waterflooding performance in layered-composite reservoirs is essentially performance in layered-composite reservoirs is essentially controlled by the mobility ratio.
Equations giving the pressure drop, time of breakthrough, water-front location, coverage, WOR and cumulative oil recovery in a layered-composite reservoir are presented. Application of these equations to the case of constant injection pressure, which was not treated by the original Dykstra-Parsons method, is discussed.
The prediction of waterflooding performance for a stratified reservoir as been the subject of many investigations. Stiles presented an approach for predicting oil recovery and water cut presented an approach for predicting oil recovery and water cut from such stratified systems. The approach assumes: the mobility ratio is unity, piston-like displacement, all beds have the same porosity and the same relative permeabilities to water behind the porosity and the same relative permeabilities to water behind the flood and to oil ahead of the flood. Dykstra and Parsons' introduced a semi-empirical treatment for calculating the recovery of oil by waterflooding stratified reservoirs. Their correlations reflect the effect of initial fluid saturations, mobility ratios, and permeability variations on the recovery of oil by water injection. Kufus and Lynch developed an approach by combining the Dykstra- Parsons method and the Buckley-Leverett theory. Snyder and Parsons method and the Buckley-Leverett theory. Snyder and Ramey extended the Buckley-Leverett theory to stratified reservoirs.
The effect of cross-flow on oil recovery due to waterflooding from stratified reservoirs has been investigated by Warren and Cosgrove and Goddin, et al. Warren and Cosgrove model considers the viscous forces and neglects both capillary and gravity forces. Goddin, et al, used a two-phase, two-dimensional model and concluded that waterflooding performance with crossflow is intermediate between the performance of a stratified reservoir with no cross-flow and that of a uniform system. Coats studied the effect of gravitational and capillary forces in the waterflooding of a heterogeneous linear reservoir of mixed permeability ordering.
All these studies are based on the assumption that the rock and fluid properties remain constant in the lateral direction. in this study a modification to the Dykstra-Parsons method to predict waterflooding performance of multi-layered composite reservoirs is presented. The modification is extended to the case of constant presented. The modification is extended to the case of constant injection pressure.
Figure 1 is a schematic representation of a layered-composite reservoir. The details of the jth layer are shown in Figure 1b. The properties of that layer are., K., ., and h, for the region that is close to the producer. The width (W) is the same for both regions in all layers.